Plasma and Fusion Research: Regular Articles

Volume 10, 1402007 (2015)

Simultaneous Measurement of Plasma Pressure Anisotropy with a
Double-Pass Thomson Scattering Diagnostic System on the TST-2
Junichi HIRATSUKAa) , Akira EJIRI, Makoto HASEGAWA1) , Yoshihiko NAGASHIMA1) ,Keishun NAKAMURA, Yuichi TAKASE, Hiro TOGASHI, Hiroshi TOJO2) ,Takashi YAMAGUCHI and TST-2 group
The University of Tokyo, Kashiwa 277-8561, Japan
Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan
2)
Japan Atomic Energy Agency, 801-1 Mukoyama, Naka-shi, Ibaraki 311-0193, Japan
1)(Received 28 March 2014 / Accepted 3 October 2014)
We have developed a double-pass Thomson scattering diagnostic system for the TST-2 spherical tokamak
device. By measuring the first- and second-pass scattering signals simultaneously, we obtained the two directionalpressures and we measured the pressure anisotropy (i.e., the ratio of the pressures) with an error of 5% - 10% formoderate density ( 2 × 1019 m−3 ) plasmas. We observed 30% and 100% anisotropy at the center and edge of
the Ohmic-heated plasmas, respectively. We propose a three-temperature Maxwellian model, in which the fitting
is better than in the shifted-Maxwellian model. The estimated plasma current density was close to the averaged
current density. The results suggest that the contribution of thermal electrons to a plasma current is large in
Ohmic-heated plasmas.
c 2015 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: Thomson scattering, double-pass configuration, pressure anisotropy, current density measurement,
TST-2
DOI: 10.1585/pfr.10.1402007

1. Introduction
The velocity distribution functions of plasma tend to
be isotropic Maxwellian distribution functions when in
equilibrium. In high temperature fusion plasmas, however, the distribution functions can be distorted due to various reasons, such as the electric field, the magnetic mirror eﬀect, wave heating, and neutral beam injection. Thisanisotropy in the velocity distribution function results ina destabilization of the ballooning modes [1] and a deformation of the plasma pressure from the flux function [2].
Although anisotropy measurement is important, the diagnostics for the plasma core have not been established.
The Thomson scattering diagnostic is a method formeasuring electron temperature and density from Thomson scattering light of a laser beam injected into a plasma.
The wavelength spectrum of the scattering light reflects the
Doppler shift of the electrons along the scattering vectork = ks − ki [3]. Here, ks and ki are the wave vectorsof the scattered light and the injected laser, respectively.
The width of the spectrum represents the electron temperature, and the intensity of the scattering light is proportional to the electron density. A method to measure theplasma pressure anisotropy with Thomson scattering diagnostics, proposed in 1979 [4], was discussed recently indetail [5,6]. Several experiments using Thomson scattering
author’s e-mail: hiratsuka.junichi@jaea.go.jpa) Present address: Japan Atomic Energy Agency, 801-1 Mukoyama,Naka-shi, Ibaraki 311-0193, Japandiagnostics have been performed to measure plasma pressure anisotropy and the shape of the plasma velocity distribution function [7–12]. These studies used visible highpower lasers, that are not suitable for fusion plasma diagnostics. In addition, the reproducibility of the plasma discharge is still uncertain since pe,⊥ and pe,|| were not measured simultaneously.
A two-directional plasma pressure diagnostic, thedouble-pass Thomson scattering diagnostic, with a
Nd:YAG laser, was recently developed [13, 14]. The
Nd:YAG laser is more appropriate than visible lasers due
to its high repetition rate and its wavelength region (infrared). Furthermore, pe,⊥ and pe,|| are measured almost
simultaneously. In order to measure two-directional velocity distribution functions, the direction of ks or ki should
be changed for each measurement. A laser beam passes
through a plasma once in a standard Thomson scattering
diagnostic. In contrast, the laser beam is reflected back to
the plasma in the double-pass scheme. Then, the forward
and the backward scattering light can be measured by single collection optics. Therefore, Thomson scattering lights
with two directions of ki can be measured, and we can obtain the two-directional velocity distribution functions of
the thermal electrons (Fig. 1).
However, there are problems for double-pass measurements using a Nd:YAG laser. First, the number ofwavelength channels is restricted in Nd:YAG Thomson
scattering because of the low signal level. Second, detec-

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Fig. 1 Schematic of the geometry of double-pass Thomson scattering.

tor and electric circuit must be fast-response and low-noise
to separate the two pulses of the Thomson scattering lights
within a very short time interval. In addition, we must consider the shape of the velocity distribution function when
we apply this method to current density diagnostics. Although a current density profile was obtained in [12], theauthors also reported that the estimation from the shiftedMaxwellian fitting was diﬀerent from that of the momentof the velocity distribution in an Ohmic-heated plasma.
In this paper, we report an accurate diagnostic of pressure anisotropy with few wavelength channels by using afast and low-noise detection system and by evaluating measurement error in detail. We also investigated the velocity
distribution function in an Ohmic-heated plasma, and describe its application to current density measurement.

2. Double-Pass Thomson System
We have developed and previously reported a doublepass Thomson scattering diagnostic system [13, 14] on a
TST-2 spherical tokamak device (Ip  100 kA, Bt < 0.2 T,
R0 = 0.38 m and a = 0.25 m) [15]. This system consistsof laser injection optics, collection optics, and a detection
system. We used a Nd:YAG laser with a beam energyof 1.6 J and a pulse width of 10 ns. The laser is injected
into the plasma and reflected back by a spherical mirror(Fig. 2). The Thomson scattering lights, excited by thelaser beam in the first- and second-passes, are collectedby a spherical collection mirror (diameter 600 mm, focal
length 300 mm) and then transferred into polychromators
by fibers with a numerical aperture of 0.37. There are six
wavelength channels in each polychromator. Each channel consists of an interference filter, an avalanche photodiode (Si APD S8890-30, Hamamatsu Photonics), and a
two-stage amplifier. The detected signal is digitized by an
oscilloscope. The forward- and backward-scattering pulses
are separated clearly by a fast and low-noise detection system [16]. In this system, the velocity distribution functions
that are nearly perpendicular and parallel to the magnetic
field can be measured within 40 ns (Fig. 3). The forward
and backward Thomson scattering signal intensities are estimated separately by fitting a superposition of two singlepass Thomson scattering waveforms. Details of the wave-

Fig. 2 Schematic of the laser path.

Fig. 3 Typical signals of a forward and a backward Thomson
scattering light for each wavelength channel of a polychromator. Blue symbols with error bars represent signals with random noise including shot noise from straylight and thermal noise. Red curves denote fitting results
to a template waveform [13].

form fitting are described in [13].
Spectra obtained by the first- and second-passes reflect velocity distribution functions with diﬀerent directions parallel to kfirst and ksecond , respectively. kfirst andksecond are the scattering vectors of the first- and secondpasses, respectively. Furthermore, the scattering angles are
diﬀerent for the first- and second-passes. Spectra from aplasma with a temperature of 100 eV are plotted in Fig. 4,
as are the sensitivities of each polychromator wavelength
channel.
In order to prevent the laser beam from returning to thelaser device, the returning laser path (second-pass) is displaced from the injecting laser path (first-pass). The measurement points in the first- (lower field side) and secondpasses (higher field side) are about 10 mm apart, along theradial direction.

3. Error Estimation
Velocity distribution functions should be measured
precisely for the diagnostics of pressure anisotropy and1402007-2

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Fig. 4 Thomson scattering spectra measured by the first- (red)and second-passes (blue) from a plasma with an electron
temperature of 100 eV. The sensitivities of the polychromator wavelength channels (see Fig. 3) are also plotted.

plasma current density. However, the Thomson scattering
signal is weak. Therefore, error estimation is important.
An error may be classified into systematic error andrandom error. The main sources of systematic error are
variations in environmental temperature and bias voltage.
These variations can pose problems because the sensitivityof the detector (APD) depends on these factors. With thissystem, the environmental temperature and bias voltage
are controlled to an accuracy of less than 1◦ C and 0.5 V,
respectively, which reduces the systematic error to 1.3%.
Another systematic error comes from the 10 mm diﬀerence in the observation points for the forward and backward Thomson scattering measurements. The total systematic errors including these eﬀects are 1.4% and 9.1% at
R = 389 mm and R = 220 mm, respectively. On the other
hand, the main sources of random noise are shot noise fromstray signals, shot noise from a Thomson scattering signal,
thermal noise [16], and errors in the waveform fitting. We
reduced stray light with appropriate apertures (baﬄe plates
and movable apertures in Fig. 2) to mask the stray light on
the laser path. Figure 5 shows typical time-averaged straylight signals. We obtained the Thomson scattering signal
by subtracting the averaged stray light signal from the measured signal. When we added all the wavelength channel
signals, we found that the level of the stray light signal wasless than about 5% of the Thomson scattering signal. The
number of detected photons in the experiments describedin this paper was at least more than 1000, which means thatthe error from the shot noise from stray light was less than
0.8%.
The dominant random noise sources were shot noisefrom Thomson scattering light, thermal noise, and error
in the waveform fitting. The level of shot noise depends
on the detected photon number, whereas thermal noise isindependent of it. Therefore, total random noise σrandom

Fig. 5 Comparison of the intensity of the measured scattering
signals (black) and the averaged stray light signals (red).
The diﬀerence in DC levels between the black and the red
curves represents the background plasma light.

Fig. 6 Average vs. relative error of 1024 Raman scattering signals (double logarithmic plot).

can be expressed as
σrandom =√ηshot μ + αthermal ,(1)

where μ is the signal intensity. ηshot is a coeﬃcient reflecting the shot noise, and α is a constant reflecting the thermal
noise and the error in the waveform fitting. We estimatedthe constants by measuring the rotational Raman scattering of nitrogen. The scattering from nitrogen at constantpressure can be used as a light source of constant intensity.
The average and standard deviation of 1024 Raman scattering signals correspond to μ and σrandom , respectively. Figure 6 shows the relation between the measured signal intensity and the random error values. We fitted the relation
to the Eq. (1). Diamonds (), squares (), triangles (),and crosses (×) represent the four wavelength channels of
the polychromators. The black, red, and blue symbols indicate three diﬀerent polychromators. The diﬀerences in
the lines are caused by the diﬀerence in the sensitivities of

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the polychromator channels.
The random error of each channel can be calculated
from Eq. (1). For ne = 2 × 1019 m−3 (Fig. 3), the random
errors in the electron temperature measured by the firstand second-passes (T e,first and T e,second ) are 2.4% and 4.5%,
respectively, leading to a random temperature anisotropy
error of Δ(T e,⊥ /T e,|| ) = 5.1%. As the systematic errors areabout 1.4% and 9.1%, in this case, the total measurement
errors were 5% and 10% at R = 389 mm and R = 220 mm,
respectively.

4. Simulations and Models
The velocity distribution in an Ohmic-heated plasma
is distorted by an external electric field along the toroidal
direction [17]. Thus, a modeling of the distribution which
expresses this distortion is necessary to reconstruct the distribution from the Thomson scattering signals. We calculated the velocity distribution function with the FokkerPlanck code CQL3D [18] for an Ohmic-heated plasma in
the TST-2 device. In general, the shifted-Maxwellian isassumed for such a measurement. However, the calculation results suggest that there is no shift but the distribution is similar to that of Maxwellian’s for diﬀerent temperatures along ve,|| > 0, ve,|| < 0, and ve,⊥ . In order torepresent such a distorted distribution, we propose a threetemperature Maxwellian model, in which the velocity distribution function is expressed as follows:

Fig. 7 A typical fitting result to the three-temperature
Maxwellian model for the first- (left) and second- (right)
pass scattering signals. Black squares with error bars
denote the detected signals and red curves indicate thefitting results.

Table 1 The scattering angle (θ) and the angle between the scattering vector k and the toroidal direction (φ) at eachmeasurement point.

R [mm]
220389

θfirst138.9◦
124.7◦

θsecond
40.1◦
55.1◦

φfirst128.2◦
91.3◦

φsecond
38.2◦
1.25◦



m
m 2
exp −
v
,
fe (ve,⊥ ) = ne,⊥
2πkT e,⊥2kT e,⊥ e,⊥



m
m
fe (ve,|| > 0) = ne,coexp −
v2e,|| ,2πkT e,co
2kT e,comm
fe (ve,|| < 0) = ne,ctr
exp −
v2e,|| .
2πkT e,ctr
2kT e,ctr(2)Here, we defined the polarity as positive ve,|| > 0 whenthe electron is co-directed with the acceleration directionof the Ohmic electric field. We refer to the ve,|| > 0
and ve,|| < 0 directions as the co- and counter- (ctr-) directions, respectively. Pressures are defined as pe,⊥ =ne,⊥ T e,⊥ , pe,co = ne,co T e,co and pe,ctr = ne,ctr T e,ctr . Figure 7 shows a typical fitting result for a double-pass measurement into the three-temperature Maxwellian model.
We obtained the data in a normal electric field discharge(blue in Fig. 9). ne,first = (2.07 ± 0.03) × 1019 m−3 andne,second = (2.06 ± 0.06) × 1019 m−3 , T e,first = 120 ± 3 eV
and T e,second = 135 ± 6 eV.

5. Experimental Results
We measured the pressure anisotropy of the Ohmicheated plasma at the plasma center (R = 389 mm) and edge
(R = 220 mm) on TST-2 with the double-pass Thomson
scattering system. The scattering angles and the angle between the scattering vector k and the toroidal direction at

Fig. 8 Time slices of the total plasma current (Ip ) and loop voltage (Vloop ) of a typical Ohmic-heated plasma in TST-2
with normal (blue) and reversed (red) electric fields.

each measurement point are listed in Table 1.
Since most of the signals reflect only one side of avelocity distribution function, as shown in Fig. 4, we can
not measure pe,co and pe,ctr simultaneously. Therefore, wereversed the Ohmic electric field to invert the velocity distribution function of the plasma. Then, the plasma current is also reversed (Fig. 8). We then measured pe,first andpe,second at the plasma center and edge with normal and re-

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Table 2 Averaged χ2 values of the fitting. 3T and Shift indicate the three temperature-Maxwellian model and theshifted-Maxwellian model, respectively.

χ2 /(n − m) Data number

R [mm] Models n m
389
389
220
220

3T
Shift
3T
Shift

6
6
6
6

2
2
2
2

1.55
2.01
1.84
2.83

382
382
571
571

Furthermore, we compared the chi-squared value
χ2 of the three-temperature Maxwellian model and theshifted-Maxwellian model. χ2 represents the goodness offit, defined as follows:χ2 = (yi − yfit,i )2iFig. 9 Relationship between the parameters measured by the
first- and the second-pass at the plasma center (R =389 mm, left) and at the edge (R = 220 mm, right) withnormal (blue) and reversed (red) electric field. Pressure(a, d), temperature (b, e) and (c, f) density are shown.

versed Ohmic fields (Fig. 9). In the TST-2 configuration,
we measured pressures pe,⊥ and pe,|| (pe,co or pe,ctr ) by the
first- and second-passes at the plasma center, respectively.
We measured pe,co and pe,ctr with the second-pass in thenormal and the reversed electric fields experiment, respectively. We note here that kfirst (ksecond ) is not purely perpendicular (parallel) to the magnetic field at the plasma edge(see Table 1). In Fig. 9, each symbol corresponds to one
measurement of a plasma discharge. Figure 9 shows thedata scatter. The ranges for plasma density, temperatureand the Ohmic electric field are wide because we took measurements for several diﬀerent discharge timings. These
diﬀerences may be the cause of the scatter.
Figure 9 shows a clear relation of pe,co > pe,⊥ > pe,ctr ,which is qualitatively consistent with the CQL3D code calculation. The pressure anisotropies pe,|| /pe,⊥ are around
30% and 100% at the plasma center and edge, respectively.
Note that the anisotropy at the edge might be larger because the directions of the measurement are not purely perpendicular (parallel) to the magnetic field. The large measured anisotropy cannot be explained by the 5% and 10%
measurement errors at the plasma center and edge, respectively.

σ2i,where yi , yfit,i , and σi are the Thomson scattering signal,
the resultant value of fitting, and the measurement error,
respectively. i is the index of a polychromator wavelength
channel. We estimated σi from the relation in Eq. (1). The
results are listed in Table 2. n and m indicate the numberof wavelength channels and the number of fitting parameters, respectively. χ2 denotes the averaged value of χ2
for all data. As a result, fitting to the three-temperature
Maxwellian model is better than the fitting to the shiftedMaxwellian model in both cases. However, there is a finite
diﬀerence between χ2 and n − m, which suggests thateither more parameters or a more appropriate model is required.
Using the three-temperature Maxwellian model, we
calculated the current density of the thermal electrons fromthe results shown in Fig. 9. We derived the current density
je from Eq. (2) asje ≡ ev|| fe (v|| )dv||



k 
=e
ne,co T e,co − ne,ctr T e,ctr .
2πm

(3)

In order to investigate the dependence of je on the plasma
resistivity η, we define η as√
2 Zeﬀ e2 m1/2
e
ln Λ.
(4)
η=
12π3/2 2 T 3/2
0e,firstZeﬀ , e, me , 0 and ln Λ are the eﬀective charge, the elementary charge, the electron mass, the vacuum permittivity, and the Coulomb logarithm, respectively. Here, we
assume Zeﬀ = 1.
Since only pe,co or pe,ctr can be measured for one
plasma discharge, we assumed that the plasma parameters
depend on T e,first ( T e,⊥ ). Then we divided the T e,first data
into every 10 eV and 5 eV intervals for the plasma center

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first measurement of a relatively large electron pressure
anisotropy in high temperature plasmas. The fitting to thethree-temperature Maxwellian model was better than to theshifted-Maxwellian model, which is qualitatively consistent with the Fokker-Planck code calculation. We calculated the electron current density of the plasma using thethree-temperature model. The resulting values are close to
the spatially-averaged current density, which suggests thatthe contribution of thermal electrons to the plasma current is relatively large in Ohmic-heated plasmas. These
results contribute to the understanding of the anisotropyof electron velocity distribution functions and demonstrate
the possibility of measuring current density with Thomson
scattering diagnostics.

Acknowledgments
Fig. 10 The relation between je and η at the plasma center andthe edge. Only the data of which the number of measurement is more than 10 is plotted. Sky blue hatchedareas represent the range of jave in the experiments.

and edge, respectively. In each group, we averaged thecorresponding T e,second , ne,first , and ne,second , and then substituted the averaged values into Eqs. (3) and (4). Figure 10
shows the relations between je and η. The hatched areas represent the spatially-averaged current density jave =Ip /πa2 in the experiments. The measured current density
value is close to that of jave . This result suggests that thecontribution of thermal electrons (not fast electrons) to thecurrent density is relatively large in Ohmic-heated plasmas.

6. Summary
We developed a double-pass Thomson scattering diagnostic system on the TST-2, evaluated the systematicand random errors, and found the measurement error to bearound 5 - 10% for plasmas with a density of 2 × 1019 m−3 .
We observed a finite diﬀerence between pressures perpendicular and parallel to the magnetic field. The co-directed(i.e., the direction of electron acceleration) parallel pressure was almost always higher than the perpendicular pressure, and the counter-directed parallel pressure was almost always lower than the others. There was a pressure
anisotropy of around 30% at the plasma center, while atthe plasma edge it was around 100%. This represents theThis work was supported by the Japan Society for the
Promotion of Science (JSPS) Grant-in-Aid for Scientific
Research Nos. 24656556 and 21226021 and by the National Institute for Fusion Science (NIFS) Collaborative
Research Program No. NIFS12KUTR078.
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